Preheat oven to 450°F with oven rack positioned 8 inches from heat source. Place salmon, skin side down, in center of a rimmed baking sheet lined with parchment paper. Sprinkle with pepper and 1/2 teaspoon of the salt. Stir together horseradish, capers, shallot, and 2 tablespoons of the oil in a bowl until combined. Spread mixture over tops of salmon, pressing lightly to adhere. Spread tomatoes around salmon, and drizzle with 2 tablespoons oil.
Roast in preheated oven until a thermometer inserted in thickest portion of salmon registers 130°F and tomatoes have burst, about 18 minutes. Increase oven temperature to high broil (do not remove baking sheet). Broil until tomatoes and topping on salmon are browned, about 2 minutes.
Toss arugula with remaining 1 teaspoon oil. Sprinkle tomatoes with arugula, pistachios, thyme, and remaining 1/4 teaspoon salt, and serve.